Born cavity model

The energy curves in Figure 22 are closely related to the Marcus-Hush theory for electron transfer. The formalism we employ emphasizes a dipole model for the solute solvent interaction, i.e., an Onsager cavity model. However, a Born charge model based on ion solvation as something in between [135] would be essentially equivalent because we do not attempt to calculate Bop and Bor but rather determine them empirically. 

The generalized Born solvation models o " " take account of specific water interactions explicitly and give excellent agreement in the AMl-SMl and PM3-SM3 cases AMl-SMl is less successful, albeit still improved over the most reasonable BKO treatment. Cavity radii are not an issue for these models. 

The simplest reaction field model, known as the Born model, consists of a spherical cavity where only the net charge and the dipole moment of the molecule are considered. When the solute is represented by a set of atomic charges the model is often called Generalized Born (GB) Model. Ellipsoidal cavities can also be employed as in the early Kirkwood-Westheimer model. The main advantage of these simple models is that [Eq. (7.12)] can be computed analytically. Unfortunately, they are of limited accuracy. 

In order to obtain the matrix equations above, one must decide how to construct, and subsequently discretize, the cavity surface. The most widely used methods take the cavity to be a union of atom-centered spheres [77], as suggested in Fig. 11.1(a). The electrostatic solvation energy is quite sensitive to the radii of these spheres (it varies as in the Born ion model), and highly parameterized constructions that exploit information about the bonding topology [6] or the charge states of the atoms [31] are sometimes employed. The details of these parameterizations are beyond the scope of the present work, especially given that careful reconsideration of these parameters is probably necessary for classical biomolecular electrostatics calculations. 

A problem of molecular-shaped SCRF models is the absence of an analytical solution for the reaction field. One line of development was the search for an approximate expression for the dielectric interaction energy of a solute in a molecular-shaped cavity, without the need for explicit calculation of the solvent polarization. These models were summarized as generalized Born (GB) approximations [22,30]. The most popular of these models... 

In the Generalized Born model [2-5], the solvent is described in a extremely simplified way and there is no mutual polarization between solute and solvent. The Onsager model [6] allows for solute-solvent polarization, but the description of the cavity and of the solvent is still very crude. 

This is a generalization of the Onsager reaction field model for a point dipole inside a spherical cavity. For charged solutes, one should also include an ionic Born term, derived by... 

Current developments of the MPE continuum model focus on the combination of a multicentric multipole moment expansion of the reaction field combined with a discrete charge representation of the solute charge distribution fitting the electrostatic potential. This scheme leads to a simple formulation that parallels generalized-Born (GB) methods, though in the MPE-GB approach, the only parameter that needs to be defined is the cavity surface [76]. 

We developed the Analytical Generalized Born plus Non-Polar (AGBNP) model, an implicit solvent model based on the Generalized Born model [37-40,44, 66] for the electrostatic component and on the decomposition of the nonpolar hydration-free energy into a cavity component based on the solute surface area and a solute-solvent van der Waals interaction free energy component modeled using an estimator based on the Born radius of each atom. 

The aqueous solvation free energies of the four tautomers available to the 5-(2H)-isoxazolone system have also been studied using a variety of continuum models (Table 7). Hillier and co-workers - " have provided data at the ab initio level using the Born-Kirkwood-Onsager model, the classical multipolar expansion model (up to I = 7), and an ab initio polarized continuum model. We examined the same BKO model with a different cavity radius and the AMl-SMl and AMl-SMla o- models, and Wang and Ford have performed calculations with the AMl-PCM model. 

In the context of generalized Born models, Friesner and coworkers [88] have experimented with a cavity defined as an isosurface of a pseudo-density, d(r), that is expressed as a sum of atom-centered Gaussians ... 

In the future, DESMO should be tested with finite ion size and compared to numerical solution of the LPBE using a cavity surface (defined by the van der Waals radii Ri) that does not coincide with the ion exclusion surface (defined by Rj + Rion)- Finite ion size has incorporated into Generalized Born models, however, via the ion exclusion factors in Eq. (11.31) [46], These models are discussed in the next section. 

The quantity in Eq. (11.33) denotes the "perfect" effective Born radius for q, [64], the efficient and accurate computation of which is a major part of the development of GB models. To define let denote the exact polarization energy (obtained by solving Poisson s equation) for the atomic charge q, in a cavity representative of the entire molecule. (That is, we turn off all charges... 

The simplest reaction field model is a spherical cavity, where only the lowest order electric moment of the molecule is taken into account. For a net charge in a cavity of radius a, the difference in energy between a vacuum and a medium with a dielectric constant of e is given by the Born model. ... 

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